Radical enhancement of molecular thermoelectric efficiency

There is a worldwide race to find materials with high thermoelectric efficiency to convert waste heat to useful energy in consumer electronics and server farms. Here, we propose a radically new method to enhance simultaneously the electrical conductance and thermopower and suppress heat transport through ultra-thin materials formed by single radical molecules. This leads to a significant enhancement of room temperature thermoelectric efficiency. The proposed strategy utilises the formation of transport resonances due to singly occupied spin orbitals in radical molecules. This enhances the electrical conductance by a couple of orders of magnitude in molecular junctions formed by nitroxide radicals compared to the non-radical counterpart. It also increases the Seebeck coefficient to high values of 200 μV K−1. Consequently, the power factor increases by more than two orders of magnitude. In addition, the asymmetry and destructive phonon interference that was induced by the stable organic radical side group significantly decreases the phonon thermal conductance. The enhanced power factor and suppressed thermal conductance in the nitroxide radical lead to the significant enhancement of room temperature ZT to values ca. 0.8. Our result confirms the great potential of stable organic radicals to form ultra-thin film thermoelectric materials with unprecedented thermoelectric efficiency.


Introduction
By 2030, twenty percent of the world's electricity will be used by computers and the internet, much of which is lost as waste heat. 1 This waste heat could be recovered and used to generate electricity economically, provided materials with a high thermoelectric efficiency could be identied. [2][3][4] Despite several decades of development, the state-of-the-art thermoelectric materials 5 are not sufficiently efficient to deliver a viable technology platform for energy harvesting from consumer electronics or on-chip cooling of CMOS-based devices. 2,6 The efficiency of a thermoelectric device is proportional to a dimensionless gure of merit 7,8 ZT ¼ S 2 GT/k, where S is the Seebeck coefficient, G is the electrical conductance, T is the temperature and k ¼ k el + k ph is the thermal conductance 9 due to electrons k el and phonons k ph . Therefore low-k, high-G and high-S materials are needed. However, this is constrained by the interdependency of G, S and k. Consequently, the world record ZT is about unity 5,10 at room temperature in inorganic materials 11 which are toxic (e.g. PbTe 12 ) and their global supply is limited (e.g. Te). 13 An alternative solution is to use organic molecular scale ultra-thin lm materials.
In molecular scale junctions, electrons behave phase coherently and can mediate long-range phase-coherent tunneling even at room temperature. [14][15][16][17] This creates the possibility of engineering quantum interference (QI) in these junctions for thermoelectricity. Sharp transport resonances are mediated by QI in molecular structures. 18 This could lead to huge enhancements of G and S provided the energy levels of frontier orbitals are close to the Fermi energy (E F ) of electrode. This is evident from high power factor (S 2 G) obtained by shiing E F close to a molecular resonance in the C60 molecular junction using an electrostatic gating. 6,19 However, using a third gate electrode is not desirable in a thermoelectric (TE) device because a TE device is expected to generate power but not to consume it through the electrostatic gating. An alternative solution would be to design molecular structures such that the energy level of frontier orbitals is pushed toward the Fermi energy (E F ) of the electrode. In what follows, we demonstrate that this can be achieved using stable organic radicals. 20 The single lled orbital in radicals has a tendency to gain or donate an electron and move down in energy; therefore, its energy level has to be close to the E F of the electrode. structures with unprecedented thermoelectric efficiency. Fig. 1 shows the molecular structure of 2,2 0 -bipyridine (BPy) and 2,2 0bipyridine functionalized with tert-butyl nitroxide radical (BPyNO) cores connected to two thiobenzene anchors through acetylene linkers. BPyNO radicals have been demonstrated to be stable under ambient conditions with no decomposition for several months. 21 In order to further enhance the stability of the molecular lm formed by a massively parallel array of BPyNO, suitable encapsulation similar to that applied for 2D materials 22 can be applied. BPy is a conjugated molecule and its highest occupied molecular orbital (HOMO) is extended over the molecule (Fig. 2a). The highest occupied spin orbital (HOSO) for majority spins of BPyNO is localized on the NO fragment and neighbouring phenyl ring (Fig. 2a). Spin density calculation (see Methods) reveals that this is due to the localization of majority spins on nitroxide radicals (Fig. 2b). Note that a-HOSO (highest occupied spin orbital), a-LUSO (lowest unoccupied spin orbital), b-HOSO and b-LUSO may be referred to also as spin-up HOMO, spin-up LUMO, spin-down HOMO and spin-down LUMO, respectively.
To study transport properties of junctions formed by BPy and BPyNO between the gold electrodes, we obtain material specic mean-eld Hamiltonians from the optimised geometry of junctions using density functional theory (DFT). 23 We then combine the obtained Hamiltonians with our transport code 7,24 to calculate the transmission coefficient 7 T e (E) for electrons traversing from the hot electrode to the cold one ( Fig. 1) through BPy and BPyNO (see Computational methods). T e (E) is combined with the Landauer formula 7 to obtain the electrical conductance. At low temperatures, the conductance G ¼ G 0 T e (E F ) where G 0 is the quantum conductance and E F is the Fermi energy of the electrode. At room temperature, the electrical conductance is obtained by the thermal averaging of transmission coefficients calculated using the Fermi function (see Computational methods). Fig. 2c shows the transmission coefficient T e (E) for electrons with energy E traversing through the BPy and BPyNO junctions. The red curve in Fig. 2c shows T e for BPy. The room temperature electrical conductance of the BPy junction is ca. 4 Â 10 À4 G 0 at DFT Fermi energy (E ¼ 0 eV). The electron transport is mainly through the HOMO level because of the extended HOMO state (see Table S1 of the ESI †). Furthermore, due to the charge transport between sulphur atoms and gold electrodes, in molecular junctions formed by thiol anchors, transport occurs to be through the HOMO state. 25 Since the electronic structure of BPyNO is spin polarised, we compute the total Due to quantum interference between the transmitted wave through the backbone and reected wave by the singly occupied orbital of the pendant group, a Fano-resonance forms. This is shown by the simple tight-binding model in Fig. 3b. When a pendant orbital is attached to the one level system (Fig. 3a), two resonances are formed due to the backbone and pendant sites. The resonances are close to the energy levels of these orbitals. The resonance due to a-HOSO is close to E F in BPyNO (shown also with the grey region in Fig. 2c). The BPyNO radical has a tendency to gain (see Table S3 of the ESI †) an electron or share its electron (e.g. with a hydrogen atom to form -O-H) and minimize its energy. Fig. 4 shows the spin orbitals of the BPyNO molecular core and molecular orbitals of BPyNO with a hydrogen atom attached to oxygen to form the non-radical counterpart of BPyNO. When the hydrogen atom is detached Fig. 1 Molecular structure of a thermoelectric device where stable organic radical and non-radical molecules are placed between two hot and cold gold electrodes. Molecules consist of 2,2 0 -bipyridine (BPy) and 2,2 0 -bipyridine functionalized with tert-butyl nitroxide radical (BPyNO) cores connected to two thiobenzene anchors through acetylene linkers. from the core, the HOMO level of the non-radical BPyNO splits into two a-HOSO and b-LUSO states and moves up in energy.
The conductance of BPyNO is ca. 3 Â 10 À3 G 0 at DFT Fermi energy. Due to the new resonance transport through majority spins (see spin density plots in Fig. 2b), the conductance of BPyNO, on average, is about an order of magnitude higher than that of BPy around DFT Fermi energy. This is even higher closer to the resonance. This new resonance not only enhances the electrical conductance signicantly, but also has a large effect on the room temperature Seebeck coefficient S (Fig. 2d). Note that S is proportional to the slope of the electron transmission coefficient T e evaluated at the Fermi energy (Sav ln T(E)/vE at E ¼ E F ). 4,7 As a consequence of the sharp slope of a-HOSO resonance in BPyNO close to E F , the Seebeck coefficient increases 4 times compared to that of BPy and reaches high values of ca. +200 mV K À1 in BPyNO. The sign of S is positive as a consequence of HOSO dominated transport in BPyNO. 26 The heat is transmitted by both electrons and phonons. 3 Fig. 2e shows the thermal conductance due to electrons obtained from T e in Fig. 2c (see Computational methods). The heat transport due to electrons is higher in BPyNO but its absolute value is very low in the range of 0.6-1.5 pW K À1 compared to other molecular junctions. 3,18 In order to calculate thermal conductance due to phonons, we use material specic ab initio calculation. We calculate the transmission coefficient 7 of phonons T p (u) with energy ħu traversing through BPy and BPyNO from one electrode to the other. The thermal conductance due to phonons (k p ) then can be calculated from T p (u) using a Landauer like formula (see Computational methods). Fig. 5a shows the phonon transmission coefficient T p (u) for BPy and BPyNO junctions. Clearly T p is suppressed in BPyNO compared to that of BPy for two reasons. First, the nitroxide radical makes the molecule asymmetric. Secondly, it reects transmitting phonons through the BPy backbone. Consequently, the width of the resonances decreases. 7 This is also conrmed by the simple tight binding model in Fig. 3c. Furthermore, some of the vibrational modes are suppressed e.g. modes at 6 meV, 9.5 meV and 13 meV (see movies in the ESI † that show the visualization of modes at these frequencies for both BPy and BPyNO). These two effects combined lead to a 3 times lower phonon thermal conductance in BPyNO (Fig. 5b). T p is suppressed in BPyNO such that the electron and phonon contributions to the thermal conductance become comparable. We obtain the total room temperature thermal conductance of ca. 4.5 pW K À1 in BPyNO. The thermal conductance is dominated mainly by phonons in BPy leading to a total room temperature thermal conductance of ca. 6 pW K À1 . From the obtained G, S and k, we can now compute the full thermoelectric gure of merit 7 ZT as shown in Fig. 5c. ZT enhances signicantly in the nitroxide radical functionalized junction (blue curve in Fig. 5c) compared to that of the parent BPy (red curve in Fig. 5c). A room temperature ZT of ca. 0.8 is accessible in the BPyNO   radical for a wide energy range in the vicinity of E F . This is 160 times higher than room temperature ZT ¼ 0.005 of BPy at E F .
Molecules are expected to show a high Seebeck coefficient because they pose sharp transport resonance features, thanks to their well separated discrete energy levels. However, a relatively small Seebeck coefficient has been measured in molecules so far. 3 Among them, C60 shows the highest Seebeck coefficient of about À18 mV K À1 to À20 mV K À4 . This leads to a power factor in the range of 0.03 pW per molecule. There is no thermal conductance measurement of C60 but using the predicted value, 27 a low roomtemperature ZT of 0.1 is expected. The challenge in exploiting quantum interference in molecules for thermoelectricity lies in controlling the alignment of the molecular levels and moving quantum interference induced resonances close to the Fermi level of the electrodes. Resonance transport close to the Fermi level through spin orbitals that we propose is a generic feature of stable organic radicals which can be utilised to overcome this challenge and enhance the thermoelectric efficiency of molecular junctions. The massively parallel array of BPyNO in self-assembled monolayers can then be formed to create ultra-thin molecular lms with high ZT to convert waste heat to electricity.

Conclusions
In this paper, we demonstrated for the rst time that the thermoelectric gure of merit of junctions formed by the nitroxide stable radical enhances signicantly from ca. 0.005 in the parent BPy to 0.8 in the daughter BPyNO. This enhancement is a generic feature of radicals because they create resonances close to the Fermi energy of the electrode. This ground breaking strategy can be utilized to design molecular junctions and ultrathin lm thermoelectric materials for efficient conversion of waste heat to electricity or on-chip cooling of CMOS-based technology in consumer electronic devices.

Geometry optimization
The geometry of each structure studied in this paper was relaxed to a force tolerance of 10 meVÅ À1 using the SIESTA 23 implementation of density functional theory (DFT), with a double-z polarized basis set (DZP) and the Generalized Gradient Approximation (GGA) functional with Perdew-Burke-Ernzerhof (PBE) parameterization. A real-space grid was dened with an equivalent energy cut-off of 250 Ry. To calculate molecular orbitals and spin density of gas phase molecules, we employed an experimentally parameterised B3LYP functional using Gaussian g09v2 (ref. 28) with a 6-311++g basis set and tight convergence criteria.

Electron transport
To calculate the electronic properties of the junctions, from the converged DFT calculation, the underlying mean-eld Hamiltonian H was combined with our quantum transport code, Gollum. 24 This yields the transmission coefficient T e (E) for electrons of energy E (passing from the source to the drain) via the relationship S e † L,R (E)) describes the level broadening due to the coupling between le L and right R electrodes and the central scattering region, S e L,R (E) is the retarded self-energy associated with this coupling and G R e ¼ (ES À H À S e L À S e R ) À1 is the retarded Green's function, where H is the Hamiltonian and S is the overlap matrix obtained from the SIESTA implementation of DFT. The DFT+S approach has been employed for spectral adjustment. 7 Phonon transport Following the method described in ref. 7 and 8 a set of xyz coordinates were generated by displacing each atom from the relaxed xyz geometry in the positive and negative x, y and z directions with on each atom were then calculated and used to construct the dynamical matrix D ij ¼ K ij qq 0 =M ij where the mass matrix 0 j for i s j were obtained from nite differences. To satisfy momentum conservation, the K for i ¼ j (diagonal terms) is calculated from ) describes the level broadening due to the coupling to the le L and right R electrodes, S p L,R (u) is the retarded self-frequency associated with this coupling and G R p ¼ (u 2 I À D À S p L À S p R ) À1 is the retarded Green's function, where D and I are the dynamical and the unit matrices, respectively. The phonon thermal conductance k p at temperature T is then calculated from k p ðTÞ ¼ ð2pÞ À1 ð N 0 ħuT p ðuÞðvf BE ðu; TÞ=vTÞdu where f BE (u,T) ¼ (e ħu/k B T À 1) À1 is the Bose-Einstein distribution function and ħ is reduced Planck's constant and k B is Boltzmann's constant.

Thermoelectric properties
Using the approach explained in ref. 7, the electrical conductance G ¼ G 0 L 0 , the electronic contribution of the thermal conductance k el ¼ (L 0 L 2 À L 1 2 )/hTL 0 and the Seebeck coefficient Fermi-Dirac probability distribution function f FD ¼ (e (EÀEF)/kBT + 1) À 1, T is the temperature, E F is the Fermi energy, G 0 ¼ 2e 2 /h is the conductance quantum, e is the electron charge and h is Planck's constant. The full thermoelectric gure of merit ZT is then calculated using ZT(E F ,T) ¼ G(E F ,T)S(E F ,T) 2 T/k(E F ,T) where G(E F ,T) is the electrical conductance, S(E F ,T) is the Seebeck coefficient, and k(E F ,T) ¼ k el (E F ,T) + k ph (T) is the thermal conductance due to the electrons and phonons.

Data availability
The input les to reproduce simulation data can be found at https://warwick.ac.uk/nanolab.